On partial Galois Azumaya extensions

Abstract

Let α be a globalizable partial action of a finite group G over a unital ring R, A=R⋆αG the corresponding partial skew group ring, Rα the subring of the α-invariant elements of R and α⋆ the partial inner action of G (induced by α) on the centralizer CA(R) of R in A. In this paper we present equivalent conditions to characterize R as an α-partial Galois Azumaya extension of Rα and CA(R) as an α⋆-partial Galois extension of the center C(A) of A. In particular, we extend to the setting of partial group actions similar results due to R. Alfaro and G. Szeto [1,2,3].